The Schwarz Algorithm for Spectral Methods

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1988 Italy English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Numerical Analysis, volume 25, pages 24-40 (issn: 0036-1429, eissn: 1095-7170,

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Authors: C. CANUTO; FUNARO, Daniele;

doi: 10.1137/0725003

handle: 11380/761487

The Schwarz Algorithm for Spectral Methods

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Abstract

This paper is concerned with a domain decomposition method for the Laplace equation in a square with Dirichlet boundary conditions. The method consists in a combination of the classical Schwarz alternating method with spectral methods and more precisely a Legendre-Galerkin or collocation method. Error estimates yielding geometric convergence are proven by arguments related to maximum principle.

Country

Italy

Related Organizations

University of Pavia
Italy
University of Parma
Italy
University of Modena and Reggio Emilia
Italy

Keywords

Numerical solutions to overdetermined systems, pseudoinverses, Laplace equation, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Schwartx algorithm; spectral methods, geometric convergence, collocation method, Boundary value problems for second-order elliptic equations, maximum principle, spectral methods, Legendre-Galerkin method, Spectral, collocation and related methods for boundary value problems involving PDEs, Error estimates, Schwarz alternating method, domain decomposition method

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